A376745 Numbers that are not pentagonal pyramidal numbers.

2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71

Offset: 1

Author

Chai Wah Wu, Oct 03 2024

Keywords

• nonn
• easy

Comments

Complement of A002411. Numbers not of the form k^2*(k+1)/2.

Links

• Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number

Crossrefs

Cf. A002411, A000330, A000537, A302058, A376573.

Programs

Mathematica

p=71;l=Floor[(2p)^(1/3)];Complement[Range[p],Table[n^2 (n + 1)/2, {n, 0, l}]] (* James C. McMahon, Oct 07 2024 *)

Python

from sympy import integer_nthroot
def A376745(n): return n+(m:=integer_nthroot(k:=n<<1,3)[0])-(k<=m*(m-1)*(m+2))

Formula

a(n) = n+m if 2n>m(m-1)(m+2) and a(n) = n+m-1 otherwise where m = floor((2n)^(1/3)).